Дисертації з теми "Simulation-Based Inference"

We present a general approach for Monte Carlo computation of conditional expectations of the form E[(T)|S = s] given a sufficient statistic S. The idea of the method was first introduced by Lillegård and Engen [4], and has been further developed by Lindqvist and Taraldsen [7, 8, 9]. If a certain pivotal structure is satised in our model, the simulation could be done by direct sampling from the conditional distribution, by a simple parameter adjustment of the original statistical model. In general it is shown by Lindqvist and Taraldsen [7, 8] that a weighted sampling scheme needs to be used. The method is in particular applied to the nonhomogeneous Poisson process, in order to develop exact goodness-of-fit tests for the null hypothesis that a set of observed failure times follow the NHPP of a specic parametric form. In addition exact confidence intervals for unknown parameters in the NHPP model are considered [6]. Different test statistics W=W(T) designed in order to reveal departure from the null model are presented [1, 10, 11]. By the method given in the following, the conditional expectation of these test statistics could be simulated in the absence of the pivotal structure mentioned above. This extends results given in [10, 11], and answers a question stated in [1]. We present a power comparison of 5 of the test statistics considered under the nullhypothesis that a set of observed failure times are from a NHPP with log linear intensity, under the alternative hypothesis of power law intensity. Finally a convergence comparison of the method presented here and an alternative approach of Gibbs sampling is given.

La neuroimagerie étudie l'architecture et le fonctionnement du cerveau à l'aide de la résonance magnétique (IRM). Pour comprendre le signal complexe observé, les neuroscientifiques émettent des hypothèses sous la forme de modèles explicatifs, régis par des paramètres interprétables. Cette thèse étudie l'inférence statistique : deviner quels paramètres auraient pu produire le signal à travers le modèle.L'inférence en neuroimagerie est complexifiée par au moins trois obstacles : une grande dimensionnalité, une grande incertitude et la structure hiérarchique des données. Pour s'attaquer à ce régime, nous utlisons l'inférence variationnelle (VI), une méthode basée sur l'optimisation.Plus précisément, nous combinons l'inférence variationnelle stochastique structurée et les flux de normalisation (NF) pour concevoir des familles variationnelles expressives et adaptées à la large dimensionnalité. Nous appliquons ces techniques à l'IRM de diffusion et l'IRM fonctionnelle, sur des tâches telles que la parcellation individuelle, l'inférence de la microstructure et l'estimation du couplage directionnel. Via ces applications, nous soulignons l'interaction entre les divergences de Kullback-Leibler (KL) forward et reverse comme outils complémentaires pour l'inférence. Nous démontrons également les capacité de l'inférence variationelle automatique (AVI) comme méthode d'inférence robuste et adaptée à la large dimensionnalité, apte à relever les défis de la modélisation en neuroscience
Neuroimaging investigates the brain's architecture and function using magnetic resonance (MRI). To make sense of the complex observed signal, Neuroscientists posit explanatory models, governed by interpretable parameters. This thesis tackles statistical inference : guessing which parameters could have yielded the signal through the model.Inference in Neuroimaging is complexified by at least three hurdles : a large dimensionality, a large uncertainty, and the hierarchcial structure of data. We look into variational inference (VI) as an optimization-based method to tackle this regime.Specifically, we conbine structured stochastic VI and normalizing flows (NFs) to design expressive yet scalable variational families. We apply those techniques in diffusion and functional MRI, on tasks including individual parcellation, microstructure inference and directional coupling estimation. Through these applications, we underline the interplay between the forward and reverse Kullback-Leibler (KL) divergences as complemen-tary tools for inference. We also demonstrate the ability of automatic VI (AVI) as a reliable and scalable inference method to tackle the challenges of model-driven Neuroscience

We present a non-Gaussian and non-linear state-space model for the population dynamics of cod along the Norwegian Skagerak coast, embedded in the framework of a Bayesian hierarchical model. The model takes into account both process error, representing natural variability in the dynamics of a population, and observational error, reflecting the sampling process relating the observed data to true abundances. The data set on which our study is based, consists of samples of two juvenile age-groups of cod taken by beach seine hauls at a set of sample stations within several fjords along the coast. The age-structure population dynamics model, constituting the prior of the Bayesian model, is specified in terms of the recruitment process and the processes of survival for these two juvenile age-groups and the mature population, for which we have no data. The population dynamics is specified on abundances at the fjord level, and an explicit down-scaling from the fjord level to the level of the monitored stations is included in the likelihood, modelling the sampling process relating the observed counts to the underlying fjord abundances.

We take a sampling based approach to parameter estimation using Markov chain Monte Carlo methods. The properties of the model in terms of mixing and convergence of the MCMC algorithm and explored empirically on the basis of a simulated data set, and we show how the mixing properties can be improved by re-parameterisation. Estimation of the model parameters, and not the abundances, is the primary aim of the study, and we also propose an alternative approach to the estimation of the model parameters based on the marginal posterior distribution integrating over the abundances.

Based on the estimated model we illustrate how we can simulate the release of juvenile cod, imitating an experiment conducted in the early 20th century to resolve a controversy between a fisherman and a scientist who could not agree on the effect of releasing cod larvae on the mature abundance of cod. This controversy initiated the monitoring programme generating the data used in our study.

Transportation Engineers have recently begun to incorporate statistical and machine learning approaches to solving difficult problems, mainly due to the vast quantities of data collected that is stochastic (sensors, video, and human collected). In transportation engineering, a transportation system is often denoted by jurisdiction boundaries and evaluated as such. However, it is ultimately defined by the consideration of the analyst in trying to answer the question of interest. In this dissertation, a transportation system located in Jackson, Wyoming under the jurisdiction of the Grand Teton National Park and recognized as the Moose-Wilson Corridor is evaluated to identify transportation-related factors that influence its operational performance. The evaluation considers its unique prevalent conditions and takes into account future management strategies. The dissertation accomplishes this by detailing four distinct aspects in individual chapters; each chapter is a standalone manuscript with detailed introduction, purpose, literature review, findings, and conclusion. Chapter 1 provides a general introduction and provides a summary of Chapters 2 – 6. Chapter 2 focuses on evaluating the operational performance of the Moose-Wilson Corridor's entrance station, where queueing performance and arrival and probability mass functions of the vehicle arrival rates are determined. Chapter 3 focuses on the evaluation of a parking system within the Moose-Wilson Corridor in a popular attraction known as the Laurance S. Rockefeller Preserve, in which the system's operational performance is evaluated, and a probability mass function under different arrival and service rates are provided. Chapter 4 provides a data science approach to predicting the probability of vehicles stopping along the Moose-Wilson Corridor. The approach is a machine learning classification methodology known as "decision tree." In this study, probabilities of stopping at attractions are predicted based on GPS tracking data that include entrance location, time of day and stopping at attractions. Chapter 5 considers many of the previous findings, discusses and presents a developed tool which utilizes a Bayesian methodology to determine the posterior distributions of observed arrival rates and service rates which serve as bounds and inputs to an Agent-Based Model. The Agent-Based Model represents the Moose-Wilson Corridor under prevailing conditions and considers some of the primary operational changes in Grand Teton National Park's comprehensive management plan for the Moose-Wilson Corridor. The implementation of an Agent-Based Model provides a flexible platform to model multiple aspects unique to a National Park, including visitor behavior and its interaction with wildlife. Lastly, Chapter 6 summarizes and concludes the dissertation.
Doctor of Philosophy
In this dissertation, a transportation system located in Jackson, Wyoming under the jurisdiction of the Grand Teton National Park and recognized as the Moose-Wilson Corridor is evaluated to identify transportation-related factors that influence its operational performance. The evaluation considers its unique prevalent conditions and takes into account future management strategies. Furthermore, emerging analytical strategies are implemented to identify and address transportation system operational concerns. Thus, in this dissertation, decision support tools for the evaluation of a unique system in a National Park are presented in four distinct manuscripts. The manuscripts cover traditional approaches that breakdown and evaluate traffic operations and identify mitigation strategies. Additionally, emerging strategies for the evaluation of data with machine learning approaches are implemented on GPS-tracks to determine vehicles stopping at park attractions. Lastly, an agent-based model is developed in a flexible platform to utilize previous findings and evaluate the Moose-Wilson corridor while considering future policy constraints and the unique natural interactions between visitors and prevalent ecological and wildlife.

Application integration is a process of bringing of data or functionality from one program together with that from another application programs that were not initially created to work together. Recently, the integration of numerical simulation solvers gained the importance. Integration within this domain has high complexity due to the presence of non-standard application interfaces that exchange complex, diverse and often ambiguous data. Nowadays, the integration is done mostly manually. Difficulties of the manual process force to increase the level of automation of the integration process. The author of this dissertation created a methodology and its software implementation for semi-automated (i. E. Partially automated) application integration. Application interfaces are usually represented by their syntactical definitions, but they miss the high-level semantics of applicative domains - human understanding on what the software does. The author proposes to use formal specifications (ontologies) expressed in Description Logics in order to specify software interfaces and define their high-level semantics. The author proposes a three-tier informational model for structuring ontologies and the integration process. This model distinguishes among computation-indeoendent domain knowledge (domain ontology), platform-independent interface specifications (interface ontology) and platform-specific technological integration information (technological ontology). A mediation ontology is defined to fuse the specifications. A reasoning procedure over these ontologies searches for semantic links among syntactic definitions of application interfaces. Connectors among applications are generated using the information about semantic links. Integrated applications communicate later via the connectors. The author designed a meta-model based data manipulation approach that facilitates and supports the software implementation of the integration process.

Battery energy management plays a crucial role in fuel economy improvement of charge-sustaining parallel hybrid electric vehicles. Currently available control strategies consider battery state of charge (SOC) and driver’s request through the pedal input in decision-making. This method does not achieve an optimal performance for saving fuel or maintaining appropriate SOC level, especially during the operation in extreme driving conditions or hilly terrain. The objective of this thesis is to develop a control algorithm using forthcoming traffic condition and road elevation, which could be fed from navigation systems. This would enable the controller to predict potential of regenerative charging to capture cost-free energy and intentionally depleting battery energy to assist an engine at high power demand. The starting point for this research is the modelling of a small sport-utility vehicle by the analysis of the vehicles currently available in the market. The result of the analysis is used in order to establish a generic mild hybrid powertrain model, which is subsequently examined to compare the performance of controllers. A baseline is established with a conventional powertrain equipped with a spark ignition direct injection engine and a continuously variable transmission. Hybridisation of this vehicle with an integrated starter alternator and a traditional rule-based control strategy is presented. Parameter optimisation in four standard driving cycles is explained, followed by a detailed energy flow analysis. An additional potential improvement is presented by dynamic programming (DP), which shows a benefit of a predictive control. Based on these results, a predictive control algorithm using fuzzy logic is introduced. The main tools of the controller design are the DP, adaptive-network-based fuzzy inference system with subtractive clustering and design of experiment. Using a quasi-static backward simulation model, the performance of the controller is compared with the result from the instantaneous control and the DP. The focus is fuel saving and SOC control at the end of journeys, especially in aggressive driving conditions and a hilly road. The controller shows a good potential to improve fuel economy and tight SOC control in long journey and hilly terrain. Fuel economy improvement and SOC correction are close to the optimal solution by the DP, especially in long trips on steep road where there is a large gap between the baseline controller and the DP. However, there is little benefit in short trips and flat road. It is caused by the low improvement margin of the mild hybrid powertrain and the limited future journey information. To provide a further step to implementation, a software-in-the-loop simulation model is developed. A fully dynamic model of the powertrain and the control algorithm are implemented in AMESim-Simulink co-simulation environment. This shows small deterioration of the control performance by driver’s pedal action, powertrain dynamics and limited computational precision on the controller performance.

This thesis is divided in four chapters. The two first chapters introduce a parametric quantile-based estimation method of univariate heavy-tailed distributions and elliptical distributions, respectively. If one is interested in estimating the tail index without imposing a parametric form for the entire distribution function, but only on the tail behaviour, we propose a multivariate Hill estimator for elliptical distributions in chapter three. In the first three chapters we assume an independent and identically distributed setting, and so as a first step to a dependent setting, using quantiles, we prove in the last chapter the asymptotic normality of marginal sample quantiles for stationary processes under the S-mixing condition.

The first chapter introduces a quantile- and simulation-based estimation method, which we call the Method of Simulated Quantiles, or simply MSQ. Since it is based on quantiles, it is a moment-free approach. And since it is based on simulations, we do not need closed form expressions of any function that represents the probability law of the process. Thus, it is useful in case the probability density functions has no closed form or/and moments do not exist. It is based on a vector of functions of quantiles. The principle consists in matching functions of theoretical quantiles, which depend on the parameters of the assumed probability law, with those of empirical quantiles, which depend on the data. Since the theoretical functions of quantiles may not have a closed form expression, we rely on simulations.

The second chapter deals with the estimation of the parameters of elliptical distributions by means of a multivariate extension of MSQ. In this chapter we propose inference for vast dimensional elliptical distributions. Estimation is based on quantiles, which always exist regardless of the thickness of the tails, and testing is based on the geometry of the elliptical family. The multivariate extension of MSQ faces the difficulty of constructing a function of quantiles that is informative about the covariation parameters. We show that the interquartile range of a projection of pairwise random variables onto the 45 degree line is very informative about the covariation.

The third chapter consists in constructing a multivariate tail index estimator. In the univariate case, the most popular estimator for the tail exponent is the Hill estimator introduced by Bruce Hill in 1975. The aim of this chapter is to propose an estimator of the tail index in a multivariate context; more precisely, in the case of regularly varying elliptical distributions. Since, for univariate random variables, our estimator boils down to the Hill estimator, we name it after Bruce Hill. Our estimator is based on the distance between an elliptical probability contour and the exceedance observations.

Finally, the fourth chapter investigates the asymptotic behaviour of the marginal sample quantiles for p-dimensional stationary processes and we obtain the asymptotic normality of the empirical quantile vector. We assume that the processes are S-mixing, a recently introduced and widely applicable notion of dependence. A remarkable property of S-mixing is the fact that it doesn't require any higher order moment assumptions to be verified. Since we are interested in quantiles and processes that are probably heavy-tailed, this is of particular interest.

Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished

This thesis focuses on comparing an online parameter estimator to an offline estimator, both based on the PaRIS-algorithm, when estimating parameter values for a stochastic volatility model. By modeling the stochastic volatility model as a hidden Markov model, estimators based on particle filters can be implemented in order to estimate the unknown parameters of the model. The results from this thesis implies that the proposed online estimator could be considered as a superior method to the offline counterpart. The results are however somewhat inconclusive, and further research regarding the subject is recommended.
Detta examensarbetefokuserar på att jämföra en online och offline parameter-skattare i stokastiskavolatilitets modeller. De två parameter-skattarna som jämförs är båda baseradepå PaRIS-algoritmen. Genom att modellera en stokastisk volatilitets-model somen dold Markov kedja, kunde partikelbaserade parameter-skattare användas föratt uppskatta de okända parametrarna i modellen. Resultaten presenterade idetta examensarbete tyder på att online-implementationen av PaRIS-algorimen kanses som det bästa alternativet, jämfört med offline-implementationen.Resultaten är dock inte helt övertygande, och ytterligare forskning inomområdet

In this paper I describe a motion planning technique for intelligent ground vehicles. The technique is an implementation of a path selection algorithm based on fuzzy inference. The approach extends on the motion planning algorithm known as driving with tentacles. The selection of the tentacle (a drivable path) to follow relies on the calculation of a weighted cost function for each tentacle in the current speed set, and depends on variables such as the distance to the desired position, speed, and the closeness of a tentacle to any obstacles. A Matlab simulation and the practical implementation of the fuzzy inference rule on a Clearpath Husky robot within the Robot Operating System (ROS) framework are provided.

O planejamento da operação de sistemas hidrotérmicos pode ser classificado como um problema de um sistema acoplado no tempo e no espaço, não linear, não convexo, estocástico e de grande porte. A complexidade do problema justifica a necessidade de utilização de diversas ferramentas computacionais com abordagens variadas. Este trabalho tem como objetivo a realização de estudos relacionados ao planejamento da operação energética de sistemas hidrotérmicos de geração, pela aplicação de componentes de software e de sistemas de inferência fuzzy. Pretende-se apresentar e aplicar um processo de desenvolvimento (UML Components), baseado em componentes de software, para a construção de modelos computacionais de simulação e otimização para servir de apoio ao planejamento da operação energética do sistema hidrotérmico brasileiro. O processo de desenvolvimento UML Components é aplicado de forma a nortear o desenvolvimento do software, para englobar as diferentes atividades realizadas nos fluxos de trabalho, além de incluir os vários artefatos produzidos. Como contribuição adicional, paralelamente ao uso dos componentes de software, este trabalho apresenta uma política de operação energética para reservatórios baseada em sistemas de inferência fuzzy Takagi-Sugeno. A política proposta é baseada na otimização da operação energética das usinas hidrelétricas, empregando o modelo de otimização desenvolvido. Com a operação energética otimizada, obtém-se as relações entre a energia armazenada do sistema e o volume útil operativo de cada usina a reservatório. A partir dessas relações são ajustados os parâmetros do modelo Takagi-Sugeno de ordem um. Ao optar-se por um sistema de inferência fuzzy para determinar a política de operação energética de um conjunto de reservatórios, obtém-se uma estratégia de ação/controle que pode ser monitorada e interpretada, inclusive do ponto de vista lingüístico. Outra vantagem na aplicação de sistemas fuzzy deve-se ao fato dos operadores humanos (especialistas) poderem traduzir, de forma consistente, e em termos de regras lingüísticas, o seu processo de tomada de decisões, fazendo com que a ação do sistema fuzzy seja tão fundamentada e consistente quanto a deles.
The operation planning of hydrothermal power systems can be classified as a nonseparable, nonlinear, nonconvex, stochastic and of large scale optimization problem. The complexity of this problem justifies the need for the use of various computational tools with different approaches. This work aims the accomplishment of studies related to the operation planning of hydrothermal power systems through the implementation of software components and fuzzy inference systems. It is intended to provide and implement a development process (UML Components) based on software components for building computational model of optimization and simulation to support the operation planning of the Brazilian hydrothermal power systems. The UML Components development process is a applied in a way to guide the software development to encompass different activities realized on workflows, as well as to include the various artifacts produced. As additional contribution, in parallel to the use of software components, it is intended to present an operational policy of reservoirs based on Takagi-Sugeno fuzzy inference systems. The proposed policy is based on optimization of hydropower operation, using the optimization model developed. Through the optimized operation, relations between system stored energy and the reservoir volume of each plat are obtained. With these relationships, the parameters of the Takagi-Sugeno model are adjusted. In choosing a fuzzy inference system for determining the operational policy of a set of reservoirs, it is obtained as strategy of action/control that can be monitored and interpreted including linguistic standpoint. Another benefit of the fuzzy system application refers to the fact that human specialists can consistently represent, through linguistic rules, their decision making process, making the fuzzy system action as consistent and sound as theirs.

A l’avenir, l'agriculture et l'environnement vont pouvoir bénéficier de plus en plus de données hétérogènes collectées par des réseaux de capteurs sans fil (RCSF). Ces données alimentent généralement des outils d’aide à la décision (OAD). Dans cette thèse, nous nous intéressons spécifiquement aux systèmes sensibles et adaptatifs au contexte basés sur un RCSF et un OAD, dédiés au suivi de phénomènes naturels. Nous proposons ainsi une formalisation pour la conception et la mise en œuvre de ces systèmes. Le contexte considéré se compose de données issues du phénomène étudié mais également des capteurs sans fil (leur niveau d’énergie par exemple). Par l’utilisation des ontologies et de techniques de raisonnement, nous visons à maintenir le niveau de qualité de service (QdS) des données collectées (en accord avec le phénomène étudié) tant en préservant le fonctionnement du RCSF. Pour illustrer notre proposition, un cas d'utilisation complexe, l'étude des inondations dans un bassin hydrographique, est considéré. Cette thèse a produit un logiciel de simulation de ces systèmes qui intègre un système de simulation multi-agents (JADE) avec un moteur d’inférence à base de règles (Jess)
In the future, agriculture and environment will rely on more and more heterogeneous data collected by wireless sensor networks (WSN). These data are generally used in decision support systems (DSS). In this dissertation, we focus on adaptive context-aware systems based on WSN and DSS, dedicated to the monitoring of natural phenomena. Thus, a formalization for the design and the deployment of these kinds of systems is proposed. The considered context is established using the data from the studied phenomenon but also from the wireless sensors (e.g., their energy level). By the use of ontologies and reasoning techniques, we aim to maintain the required quality of service (QoS) level of the collected data (according to the studied phenomenon) while preserving the resources of the WSN. To illustrate our proposal, a complex use case, the study of floods in a watershed, is described. During this PhD thesis, a simulator for context-aware systems which integrates a multi-agent system (JADE) and a rule engine (Jess) has been developed.Keywords: ontologies, rule-based inferences, formalization, heterogeneous data, sensors data streams integration, WSN, limited resources, DSS, adaptive context-aware systems, QoS, agriculture, environment

Bayesian melding is extended for applications to stochastic theoretical models. Agent Based models, a class of stochastic theoretical models, are investigated and it is found that the common challenge of parameter specification can be addressed with the extensions to Bayesian melding. Two versions of the extended framework are applied to the Agent Based model of bumblebee foraging behaviour published in Smolla, Alem, et al. 2016. The applications demonstrate both a comprehensive approach to parameter specification and an innovative approach to decomposing error. Posterior inference is implemented using a combination of Markov-Chain Monte Carlo and Sampling Importance Resampling algorithms.

D. Tech. Electrical Engineering.
Aims of this study is to develop a residential customers' lighting profile ANFIS-based model. This model is expected to address lighting load usage estimation in relation to the dynamic occupancy presence in a residential dwelling, which will take into account the climatic condition (natural lighting) of such an environment (e.g. South Africa) and its income. The objectives are as follows: 1. Develop an ANFIS-based residential lighting load profile model for middle income, low income and high-income earners. 2. Error reduction in residential lighting demand profile model. Performance evaluation and validation of the model using correlation and trend analysis, regression model, South Africa power utility application lighting program, non-weighted approach and comparison with other research studies (methodology).3. Reduction in / or elimination of repeated models for occupant presence and assumptions that residences are occupied at certain periods. 4. Derive meaning from complexities (behavioural trends) associated with lighting usage and extract patterns in such circumstances.